ARTICLE Received 18 Oct 2012 | Accepted 21 Aug 2013 | Published 20 Sep 2013 DOI: 10.1038/ncomms3477 Nodal quasiparticle dynamics in the heavy fermion superconductor CeCoIn5 revealed by precision microwave spectroscopy C.J.S. Truncik1, W.A. Huttema1, P.J. Turner1,S.O¨ zcan2, N.C. Murphy1, P.R. Carrie`re1, E. Thewalt1, K.J. Morse1, A.J. Koenig1, J.L. Sarrao3 & D.M. Broun1 CeCoIn5 is a heavy fermion superconductor with strong similarities to the high-Tc cuprates, including quasi-two-dimensionality, proximity to antiferromagnetism and probable d-wave pairing arising from a non-Fermi-liquid normal state. Experiments allowing detailed com- parisons of their electronic properties are of particular interest, but in most cases are difficult to realize, due to their very different transition temperatures. Here we use low-temperature microwave spectroscopy to study the charge dynamics of the CeCoIn5 superconducting state. The similarities to cuprates, in particular to ultra-clean YBa2Cu3Oy, are striking: the frequency and temperature dependence of the quasiparticle conductivity are instantly recognizable, a consequence of rapid suppression of quasiparticle scattering below Tc; and penetration-depth data, when properly treated, reveal a clean, linear temperature dependence of the quasi- particle contribution to superfluid density. The measurements also expose key differences, including prominent multiband effects and a temperature-dependent renormalization of the quasiparticle mass. 1 Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6. 2 Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, UK. 3 Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA. Correspondence and requests for materials should be addressed to D.M.B. (email: [email protected]). NATURE COMMUNICATIONS | 4:2477 | DOI: 10.1038/ncomms3477 | www.nature.com/naturecommunications 1 & 2013 Macmillan Publishers Limited. All rights reserved. ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3477 n CeCoIn5, evidence for d-wave pairing comes predominantly superconductor is quantum mechanical in origin, and the from experiments that infer the presence and location of nodes fundamental electrodynamic relation is between the current Iin the superconducting energy gap. This includes power laws density and the vector potential13. We therefore imagine a metal in zero-field heat capacity1–3 and thermal conductivity2,3, and the or superconductor perturbed by the sudden application of a field-angle dependence of heat capacity4,5, thermal conductivity6 vector potential dA. As a result, all carriers experience an impulse and quantum oscillations in the superconducting state7. These À qdA, where q is the charge of the carriers. The impulse sets the experiments are supported by evidence for spin–singlet pairing electron assembly into motion with average velocity v ¼ÀqdA/ 8,9 (decreasing Knight shift below Tc and Pauli-limited upper m*, where m* is the effective mass of the carriers. This is sketched critical field10) and by the nature of the spin-resonance peak11. in the centre column of Fig. 1 and corresponds to a current However, the emerging picture of dx2 À y2 pairing symmetry in response that opposes the applied field. A measurement of CeCoIn5 is complicated by observations on the isoelectronic current density immediately after the application of the field homologue CeIrIn5, which suggest a hybrid order parameter with reveals a diamagnetic contribution both line nodes and point nodes12. 2 Measurements of London penetration depth, lL, should nq jd ¼À dA ; ð1Þ provide a particularly clean test of nodal structure, as lL is a mà thermodynamic probe that couples preferentially to itinerant electronic degrees of freedom13–16. However, penetration-depth where n is the carrier density. Note that the strength of the data on CeCoIn5 remain surprisingly unclear. Instead of the diamagnetic contribution is proportional to n/m* andpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi is closely 2 à linear temperature dependence expected for line nodes, all related to the plasma frequency of the carriers, op ¼ nq =m E0. penetration-depth measurements to date17–19 report temperature Care must be taken with the definition of ‘sudden’: if the carriers power laws ranging from T1.2 to T1.5.Thispresentsa are excited with an arbitrarily sharp impulse, n will be the total conundrum—mechanisms such as impurity pair-breaking20,21 electron density, including core electrons, and m* the bare and nonlocal electrodynamics22 should cause a crossover to electron mass, devoid of interaction effects. For practical quadratic temperature dependence, but attempts to understand the purposes, a time scale is chosen that excites free carriers but behaviour in terms of impurity physics require unrealistically high avoids inter-band transitions. levels of disorder23. Measurements of the frequency-dependent In addition to inducing a diamagnetic current, dA changes the superfluid density offer the potential for new insights into this energy of the electron states, tilting the energy dispersion in k- problem. space by an amount dEk ¼Àq:/m*  k Á dA. Immediately after To properly understand what microwave properties can tell us excitation, the electron assembly is therefore in a non-equilibrium about a material14,24, it is helpful to visualize the measurement configuration. Equilibrium is subsequently restored by scattering process in the time domain. The Meissner response of a processes that transfer momentum to the crystal lattice. By jtot = jd jp m*v m*v m*v Metal =+ m*v m*v m*v s-wave =+ superconductor m*v m*v m*v d-wave =+ superconductor Figure 1 | Superfluid density and the paramagnetic back-flow of excitations. A momentum-space picture of the electron assembly in a superfluid density experiment, with electron-like excitations shown as filled circles and hole-like excitations as open circles. Measurements of superfluid density probe the total non-decaying current in thermal equilibrium (left-hand figures), which can be decomposed into the sum of two terms13. Immediately after the application of a vector potential dA, the Fermi sea is displaced by an amount m*v ¼ÀqdA (central figures) giving rise to a diamagnetic current. The vector potential also tilts the energy dispersion (dEk ¼Àq:/m*  k Á dA) and the resulting redistribution of electrons on the approach to equilibrium produces a paramagnetic back-flow current (right-hand figures). (a) The equilibrium current density in a metal is zero: diamagnetic and paramagnetic currents are equal and opposite, and cancel. (b) The paramagnetic back-flow current in an s-wave superconductor is strongly suppressed by the opening of an isotropic energy gap. The diamagnetic current is little changed from that in the normal state and a net current therefore flows in equilibrium, giving rise to a Meissner effect. (c)Inad-wave superconductor, the paramagnetic back-flow consists predominantly of nodal quasiparticles, which make a linear-in-temperature contribution to superfluid density. However, in CeCoIn5 the diamagnetic contribution also has temperature dependence, probably due to the material’s proximity to a quantum critical point. Isolating the nodal quasiparticle contribution requires that the current response be measured over a wide frequency range, with high frequencies probing the diamagnetic response and low frequencies the total current in equilibrium. Measurements at intermediate microwave frequencies probe the transient processes that lead to the formation of the paramagnetic back-flow current, and provide a wealth of information on the charge dynamics of the nodal quasiparticles14. 2 NATURE COMMUNICATIONS | 4:2477 | DOI: 10.1038/ncomms3477 | www.nature.com/naturecommunications & 2013 Macmillan Publishers Limited. All rights reserved. NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3477 ARTICLE studying the current response in this regime, we learn a great deal CeCoIn5, and is the reason why anomalous temperature power about electronic relaxation mechanisms in the material. laws have been obtained in earlier experiments. Our measure- At times long enough for the electron assembly to have ments reveal that the diamagnetic response (the plasma returned to equilibrium, it is useful to define the total current frequency) of CeCoIn5 weakens on cooling, in a manner density as the sum of diamagnetic and paramagnetic pieces13, corresponding to an increase in quasiparticle effective mass. That jtot ¼ jd þ jp. As discussed above, jd represents the instantaneous this occurs in CeCoIn5 is not too surprising, as it is suggestive of diamagnetic response intrinsic to the electronic states, with the proximity to a quantum critical point25,31. In addition, the tacit understanding that jd has been measured slowly enough to microwave measurements provide a detailed picture of the include only free carriers. The paramagnetic part, jp, is of a very quasiparticle charge dynamics in CeCoIn5, revealing strong different character—it captures the change in current resulting similarities to the cuprate high-temperature superconductors from the reorganization of electrons in the new equilibrium state. and pointing to a common scattering mechanism. jp is therefore very sensitive to the details of the electronic energy spectrum, making it a powerful probe of pairing symmetry in a Results superconductor. The way this process plays out is illustrated in Surface impedance. Measurements of surface impedance, Fig. 1, for a metal and for s-wave and d-wave superconductors. Zs ¼ Rs þ iXs, have been made using resonator perturba-